there is 3/4 liter of water in a pitcher then Jacob pours more water into the pitcher now there are 2 7/10 liters of water in the pitcher how many liters of water did Jacob pour into the pitcher?

Answer 1

To find out how much water Jacob poured into the pitcher, you can subtract the initial amount of water from the total amount of water after he added more.

1. Start with the initial amount of water: \[ \text{Initial amount} = \frac{3}{4} \text{ liters} \]

2. The total amount of water after pouring in more is: \[ \text{Total amount} = 2 \frac{7}{10} \text{ liters} \]

3. Convert \(2 \frac{7}{10}\) liters into an improper fraction: \[ 2 \frac{7}{10} = \frac{2 \times 10 + 7}{10} = \frac{20 + 7}{10} = \frac{27}{10} \text{ liters} \]

4. Now convert \(\frac{3}{4}\) liters to a fraction with a denominator of 10 to make the subtraction easier: \[ \frac{3}{4} = \frac{3 \times 2.5}{4 \times 2.5} = \frac{7.5}{10} \]

5. Now subtract the initial amount from the total: \[ \frac{27}{10} - \frac{7.5}{10} = \frac{27 - 7.5}{10} = \frac{19.5}{10} = \frac{195}{100} = \frac{39}{20} \]

6. Convert \(\frac{39}{20}\) to a mixed number if desired: \[ \frac{39}{20} = 1 \frac{19}{20} \text{ liters} \]

So, Jacob poured \(1 \frac{19}{20}\) liters of water into the pitcher, which is equivalent to \(1.95\) liters.

Answer 2

to verify he poured 1 9/5 liters?

Answer 3

Let's clarify and verify the calculation to ensure we find the amount of water Jacob poured into the pitcher correctly.

1. Initial Amount of Water: \[ \text{Initial amount} = \frac{3}{4} \text{ liters} \]

2. Total Amount of Water After Pouring: \[ \text{Total amount} = 2 \frac{7}{10} \text{ liters} \] Convert this to an improper fraction: \[ 2 \frac{7}{10} = \frac{2 \times 10 + 7}{10} = \frac{20 + 7}{10} = \frac{27}{10} \text{ liters} \]

3. Finding the Amount Poured: To find the amount of water Jacob poured, we subtract the initial amount from the total amount: \[ \text{Amount poured} = \text{Total amount} - \text{Initial amount} = \frac{27}{10} - \frac{3}{4} \]

4. Finding a Common Denominator: The least common multiple of 10 and 4 is 20. We will convert both fractions to have a denominator of 20: \[ \frac{27}{10} = \frac{27 \times 2}{10 \times 2} = \frac{54}{20} \] \[ \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} \]

5. Subtraction: Now, we subtract: \[ \text{Amount poured} = \frac{54}{20} - \frac{15}{20} = \frac{54 - 15}{20} = \frac{39}{20} \]

6. Converting \(\frac{39}{20}\) Back to a Mixed Number: \(\frac{39}{20}\) can be expressed as a mixed number: \[ \frac{39}{20} = 1 \frac{19}{20} \text{ liters} \]

Verification of Your Suggestion: If we convert \(1 \frac{9}{5}\) to an improper fraction: \[ 1 \frac{9}{5} = \frac{5 \times 1 + 9}{5} = \frac{5 + 9}{5} = \frac{14}{5} \] To check if \(1 \frac{9}{5}\) liters equals \(\frac{39}{20}\):

• Convert \(\frac{14}{5}\) to a fraction with a denominator of 20: \[ \frac{14}{5} = \frac{14 \times 4}{5 \times 4} = \frac{56}{20} \]

Clearly, \(\frac{39}{20} \neq \frac{14}{5}\), so \(1 \frac{9}{5}\) liters is not correct.

The amount Jacob poured is indeed \(1 \frac{19}{20}\) liters or \(\frac{39}{20}\) liters.